How to find the range of the tangent - ACT Math

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Question

What is the range of the trigonometric fuction defined by:
$f(t) = -2 \tan(3t)$ ?

Answer

For tangent and cotangent functions, the range is always all real numbers.

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Question

Find the range of: $y= 2\tan(\theta)+15$

Answer

The function $y= 2\tan(\theta)+15$ is related to $y=\tan(\theta)$ . The range of the tangent function is ${}(-\infty,\infty)$ .

The range of $y= 2\tan(\theta)+15$ is unaffected by the amplitude and the y-intercept. Therefore, the answer is ${}(-\infty,\infty)$ .

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Question

What is the range of the given trigonometric function:

$n(t) = 4\cot(2t)$

Answer

The range of a function is every value that the funciton's results take. For tangent and cotangent, the function spans from $(-\infty, \infty)$ and so the range is:

$(-\infty, \infty)$

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